Distortion when using displacement modifier
A way to obtain a smooth transition from a displaced surface to the non displaced parts is to use a vertex group and to assign the good value for the vertex weights:



Here is a view of the weights (blue = the smallest value = 0, red = the highest value = 1):



This is done with the following steps (some of them will depend on your actual mesh and the way the ring is modeled):


Create a vertex group: in the property panel, use the "plus" button as below





In the displacement modifier, assign the group:





Now we have to assign vertices to the group and fix their weights


This part depend on how the model is done. 
Here I used a parallelepiped base, set an array on it, then subsurface and a curve:



To assign the wanted vertices:


Select them
Tune the value of the weight
And assign




So going progressively to the border, while decreasing the weight value to 0, you obtain a smooth edge.

The values are visible vertex per vertex on the right side panel:



The blend file